Foundations of Economic Evaluation

Reviewing Key Concepts

Objectives/Outline

Outline

Before diving into decision trees and Markov models in Amua, I’ll spend the next ~50 minutes reviewing key concepts in economic evaluation, covering the following topics:

An example research question that can be solved using economic evaluation methods (with a brief primer on decision trees)
Types of Economic Evaluations
Cost-effectiveness analysis alongside decision trees
Competing choice problems/incremental cost-effectiveness analysis
Beyond decision trees: A brief primer on Markov models

Example Patient

Lisa is a 45 year old woman with obesity (BMI 32) who has struggled with weight management.
She does not have diabetes but is concerned about her risk for cardiovascular disease due to weight, family Hx of heart disease, and elevated cholesterol levels.
Lisa heard from a friend about Wegovy, and would like her national health program to cover it for her.

Example Patient

Lisa works as a nurse for one of the largest nonprofit health systems in the US, which recently dropped coverage of weight-loss medications due to concerns over “long-term outcomes, national coverage benchmarks, and cost-effectiveness.”
Lisa’s predicament is not uncommon …

Example Patient

If Wegovy is not covered by the National Health Programme, it will cost Lisa $1,349 per month.
More broadly, how can we reconcile the health benefits of semaglutdie against the access and affordability challenges patients now face?

Decision Trees

What outcomes might Lisa experience?

What alternative to Semaglutide might she also consider?

Let’s now quantify the possible health and cost outcomes in different states of the world …

Health Outcome

Cost Outcome

Let’s now summarize the overall health and cost outcomes

We can now map (average) health and cost outcomes to a plot

The Cost-Effectiveness Plane

The Efficiency Frontier

Efficiency Frontier

A key mechanism for decisions over how to efficiently allocate scarce resources.
Allows us to identify the set of potentially cost-effective treatments.
Strategies off the frontier cannot provide the same health benefits at equal or lower cost.

Opportunity Costs

Under a constrained budget we would have to divert resources from other worthy activities (e.g., education services, income assistance programs, other medical treatments) to cover a treatment that achieves, at best, the same health outcome.
If we select a strategy off the frontier, there is an opportunity cost and a potential loss in social welfare.

Introduction to Economic Evaluations

Economic Evaluation

Relevant when decision alternatives have different costs and health consequences.
We want to measure the relative value of one strategy in comparison to others.
This can help us make resource allocation decisions in the face of constraints (e.g., budget).

Features of Economic Evaluation

Systematic quantification of costs and consequences.
Comparative analysis of alternative courses of action.

Techniques for Economic Evaluation

Type of study	Valuation of costs	valuation of consequences	Major features
Cost analysis	Monetary units; goal to minimize cost	None	Might be useful when options are equally effective; rarely the case

Techniques for Economic Evaluation

Type of study	Valuation of costs	valuation of consequences	Major features
Cost analysis	Monetary units; goal to minimize cost	None	Might be useful when options are equally effective; rarely the case
Cost-effectiveness analysis	Monetary units	e.g., life-years gained, disability days saved, points of blood pressure reduction	Useful when considering multiple options within a budget

Techniques for Economic Evaluation

Type of study	Valuation of costs	valuation of consequences	Major features
Cost analysis	Monetary units; goal to minimize cost	None	Might be useful when options are equally effective; rarely the case
Cost-effectiveness analysis	Monetary units	e.g., life-years gained, disability days saved, points of blood pressure reduction	Useful when considering multiple options within a budget
Cost-utility analysis	Monetary units	Healthy years (quality-adjusted life-years)	Use of summary measure of health; variant of CEA

Techniques for Economic Evaluation

Type of study	Valuation of costs	valuation of consequences	Major features
Cost analysis	Monetary units; goal to minimize cost	None	Might be useful when options are equally effective; rarely the case
Cost-effectiveness analysis	Monetary units	e.g., life-years gained, disability days saved, points of blood pressure reduction	Useful when considering multiple options within a budget
Cost-utility analysis	Monetary units	Healthy years (quality-adjusted life-years)	Use of summary measure of health; variant of CEA
Cost-benefit analysis	Monetary units	Monetary units	Not making comparisons across strategies; only comparisons of costs & benefits for the same strategy (e.g., “we quantify the mortality benefits associated with the reduction in sulfates in the Indian power sector)

Cost-Effectiveness Analysis

Quantifies how to maximize the quality & quantity of life from among competing alternatives, given restricted resources.
It’s an explicit measure of value for money.
A POPULATION-LEVEL decision-making tool.

Cost-Effectiveness Analysis IS NOT

Indiscriminate cost-cutting
Downsizing
Intended to override individual-level decision-making.
The only tool for decision-making

Incremental Cost-Effectiveness Ratio

Most often used, since for most conditions there is already some available treatment.

C_1: net present value of total lifetime costs of new treatment
C_0: net present value of total lifetime costs of default treatment
E_1: effectiveness of new treatment, measured in expected life expectancy, quality-adjusted life years (QALYs) or disability-adjusted life years (DALYs), or some decision-relevant health outcome.
E_0: effectiveness of default treatment

\frac{C_1 - C_0 \quad (\Delta C)}{E_1 - E_0 \quad (\Delta E)}

Conducting a CEA

Neurologic Disease Decision Tree

Outcomes

C_{treat} = expected cost of treat everyone strategy.
C_{no treat} = expected cost of treat no one strategy.
C_{biopsy} = expected cost of biopsy strategy.

Outcomes

C_{treat} = expected cost of treat everyone strategy.
C_{no treat} = expected cost of treat no one strategy.
C_{biopsy} = expected cost of biopsy strategy.
E_{treat} = expected life expectancy of treat everyone strategy.
E_{no treat} = expected expectancy of treat no one strategy.
E_{biopsy} = expected expectancy of biopsy strategy.

Treat All vs. Treat None

Strategy: Treat No One

Treat All vs. Treat None

Strategy: Treat All

Key Takeaways (For Now)

Treatment yields higher life expectancy for those with disease, but comes at a cost.
Treatment yields lower life expectancy for those without the disease, and also comes at a cost.
Biopsy can help balance these two outcomes by better targeting treatment, but also comes with risks and costs.
Incremental CEA provides a transparent framework for quantifying and weighing these considerations.

Average Cost-Effectiveness Ratio

Special case where C_0 and E_0 are assumed to be zero.

C_1: net present value of total lifetime costs of new treatment
C_0: Assumed zero
E_1: effectiveness of new treatment, measured in expected life expectancy, quality-adjusted life years (QALYs) or disability-adjusted life years (DALYs), or some decision-relevant health outcome.
E_0: Assumed zero

\begin{aligned} ICER &= \frac{C_1 - 0}{E_1 - 0} \\ &= \frac{C_1}{E_1 } \end{aligned}

Non-Competing vs. Competing CEAs

Use of CEA in two situations

Shopping Spree: Decision problem has non-competing programs/interventions.

Each program is compared to a null alternative; therefore, you’re calculating an “average” cost-effectiveness ratio.
What can fit into the budget; breast cancer screening vs. childhood vaccination program

Use of CEA in two situations

Competing Choice: Decision problem has competing programs/interventions for the same purpose; these choices are mutually exclusive.

Two or more active alternatives in addition to the null option.
You need to calculate an “incremental cost- effectiveness ratio”, which gives us the added cost per unit of added benefit of an option, relative to the next less expensive choice.

Beyond decision trees: A brief primer on Markov models

A Simple Disease Process

Suppose we want to model the cost-effectiveness of alternative strategies to prevent a disease from occurring.
We start with a healthy population of 25 year olds and there are three health states people can experience:
1. Remain Healthy
2. Become Sick
3. Death

A Simple Disease Process

Remaining healthy carries no utility decrement (utility weight = 1.0 per cycle in healthy state)
Becoming sick carries a 0.25 utility decrement for the remainder of the person’s life (utility weight = 0.75)
Death carries a utility value of 0.0.

A Simple Disease Process

There is no cost associated with remaining healthy.
Becoming sick incurs $1,000 / year in costs.
Becoming sick increases the risk of death by 300%.

A Simple Disease Process

A country’s health institute is considering five preventive care strategies that reduce the risk of becoming sick:

Strategy	Description	Cost
A	Standard of Care	$25/year
B	Additional 4% reduction in risk of becoming sick	$1,000/year
C	12% reduction in risk	$3,100/year
D	8% reduction in risk	$1,550/year
E	8% reduction in risk	$5,000/year

Model Option 1: Decision Tree

One option would be to use a decision tree to model the expected utility and costs associated with each strategy.

Model Option 1: Decision Tree

One option would be to use a decision tree to model the expected utility and costs associated with each strategy.
What limitations do you see?

Decision tree for two full cycles.

Strategy A decision tree for 5 cycles.

Decision Trees

Pros	Cons
Simple, rapid & can provide insights

Decision Trees

Pros	Cons
Simple, rapid & can provide insights
Easy to describe & understand

Decision Trees

Pros	Cons
Simple, rapid & can provide insights
Easy to describe & understand
Works well with limited time horizon

Decision Trees

Pros	Cons
Simple, rapid & can provide insights	Difficult to include clinical detail
Easy to describe & understand
Works well with limited time horizon

Decision Trees

Pros	Cons
Simple, rapid & can provide insights	Difficult to include clinical detail
Easy to describe & understand	Elapse of time is not readily evident.
Works well with limited time horizon

Decision Trees

Pros	Cons
Simple, rapid & can provide insights	Difficult to include clinical detail
Easy to describe & understand	Elapse of time is not readily evident.
Works well with limited time horizon	Difficult to model longer (>1 cycle) time horizons

Decision Trees

Next Steps

Ideally we want a modeling approach that can incorporate flexibility and handle the complexities that make decision trees difficult/unwieldy.

Markov Models

Common approach in decision analyses that adds additional flexibility.

Pros	Cons
Can model repeated events
\quad \quad \quad \quad \quad \quad

Markov Models

Common approach in decision analyses that adds additional flexibility.

Pros	Cons
Can model repeated events
Can model more complex + longitudinal clinical events

Markov Models

Common approach in decision analyses that adds additional flexibility.

Pros	Cons
Can model repeated events
Can model more complex + longitudinal clinical events
Not computationally intensive; efficient to model and debug

Markov Models

The advantages of Markov models derive from their structure around mutually exclusive disease states.
These disease states represent the possible states or consequences of strategies or options under consideration.
Because there are a fixed number of disease states the population can be in, there is no need to model complex pathways, as we saw in the decision tree “explosion” a few slides back.

Markov Trees

It is also common to pair a Markov model with a decision tree.¹

Markov Trees

It is also common to pair a Markov model with a decision tree.¹

Markov Tree

A simple decision tree is implicit in nearly every decision analysis.

Markov Tree: Example

Treatment A:

Markov Tree: Example

Treatment A:

When choosing a model structure…

“Things should be made as simple as possible, but not simpler” - paraphrased by a lecture given by Albert Einstein at Oxford in 1933

In essence, science/models should be as simple as possible but without losing essential truth or necessary complexity.

Constructing a Markov Model

Key characteristics

Allows for health state transitions over time
Individuals can only exist in one state at a time (mutually exclusive health states)
At the beginning or end of each cycle, patients transition across health states via transition probabilities & individuals stay in health state for entire cycle length
Probability of transitioning depends on the current state (“no memory”), not on how you got there or how long you’ve been there; (though tunnel states can account for this potential limitation)
Transition probabilities typically remain constant over time (apart from embedded lifetables); though you can always add complexity & allow for more dynamic behavior (e.g., risks that change with age or treatment effects decaying)
Results report “average” of cohort

Key characteristics

“CYCLE” = Minimum amount of time that any individual will spend in a state before possible transition to another state

Steps

Define the decision problem
Conceptualize the model
Parameterize the model
Calculate or define the transition probability matrix.
Run the model

1. Define the Decision Problem

Step 1: Define the Decision Problem

We defined the decision problem earlier in this lecture, so we’ll repeat the basic objectives briefly here.

Step 1: Define the Decision Problem

Goal: model the cost-effectiveness of alternative strategies to prevent a disease from occurring.

Strategy	Description	Cost
A	Standard of Care	$25/year
B	Additional 4% reduction in risk of becoming sick	$1,000/year
C	12% reduction in risk	$3,100/year
D	8% reduction in risk	$1,550/year
E	8% reduction in risk	$5,000/year

Step 1: Define the Decision Problem

2. Conceptualize the Markov Model

Two major steps:

2a. Determine health states

2b. Determine transitions

Step 2: Conceptualize the Model

2a. Determine health states

There are three health states people can experience:
1. Remain Healthy
2. Become Sick
3. Death

Step 2: Conceptualize the Model

2a. Determine health states

There are three health states people can experience: 1. Remain Healthy 2. Become Sick 3. Death

2b. Determine transitions

Individuals who become sick cannot transition back to healthy.

Step 2: Conceptualize the Model

3. Parameterize the Model

Basic steps

3a. Determine basic model parameters

3b. Curate and define model inputs

3. Parameterize the Model

Basic steps

3a. Determine basic model parameters

Define the population (e.g., 25 year old females)
Define the Markov cycle length (e.g., 1-year cycle)
Define the time horizon (e.g., followed until age 100 or death)

3a. Define the Markov Cycle Length

Fundamentally, we’re modeling a continuous time process (e.g., progression of disease).
A discrete time Markov model “breaks up” time into “chunks” (i.e., “cycles”).
A consequence is that the model will show us what fraction start out a cycle in a given state, and what fraction end up in each state at the end of the cycle.

3a. Define the Markov cycle length

Suppose we used a one-year cycle for the healthy-sick-dead model.
Think about the underlying (continuous time) disease process.
- Recall that becoming sick substantially increases the likelihood of death.

3a. Define the Markov Cycle Length

The challenge of selecting an appropriate cycle length boils down to how we deal with competing risks.

Competing risks: individuals can transition from their current health state to two or more other health states.

3a. Define the Markov Cycle Length

The challenge of selecting an appropriate cycle length boils down to how we deal with competing risks.

If we’re not careful, we could effectively rule out the possibility of Healthy – Sick – Dead within a cycle.
The model would look like a basic Healthy – Dead transition, but they took a detour through Sick along the way!

3a. Define the Markov Cycle Length

Pros	Cons
Can model repeated events	Competing risks are a challenge
Can model more complex + longitudinal clinical events
Not computationally intensive; efficient to model and debug

3a. Define the Markov Cycle Length

It may be tempting to simply shorten the cycle length (e.g., use 1 day cycle vs. 1 year cycle).

For a 75 year horizon, how many cycles would that be?
- 27,375!!!
Any possible issues with this?

3a. Define the Markov Cycle Length

Shortening the cycle creates a computational challenge.

Base case requires 27,375 daily cycles.
Now suppose we want to run 2,000 probabilistic sensitivity analysis model runs.
- We now have 54,750,000 cycle runs to contend with!

3a. Define the Markov Cycle Length

Pros	Cons
Can model repeated events	Can only transition once in a given cycle
Can model more complex + longitudinal clinical events	Shortening the cycle can create computational challenges.
Not computationally intensive; efficient to model and debug

3a. Define the Markov Cycle Length

More challenges …

3a. Define the Markov Cycle Length

More challenges …

Markov models are “memoryless” – they don’t remember what happened before the current cycle.
- If your risk of transition to a sicker health state depends on events that happened earlier in time, the model can’t explicitly account for this.

3a. Define the Markov Cycle Length

More challenges …

There are workarounds known as “tunnel states” to get around this problem, though these are difficult to do and present their own challenges
- We won’t cover them here but can provide references if you want to explore!

3a. Define the Markov Cycle Length

Pros	Cons
Can model repeated events	Can only transition once in a given cycle
Can model more complex + longitudinal clinical events	Shortening the cycle can create computational challenges.
Not computationally intensive; efficient to model and debug	Shortening cycle can cause “state explosion” if tunnel states are used

3a. Define the Markov Cycle Length

It’s also advisable to pick a cycle length that aligns with the clinical/disease timelines of the decision problem.
- Treatment schedules.
- Acute vs. chronic condition.
Another option is to incorporate “short-run” events that happen early in the course of a disease/intervention within the decision tree, then allow the Markov model to model longer-term health consequences (pediatric appendicitis & CT scan example).

3. Parameterize the Model

3b. Curate and define model inputs

3b.i. Source and define the base case values.
3b.ii. Source and define sources of uncertainty.

3. Parameterize the Model

3b. Curate and define model inputs

Rate of disease onset
Health state utilities and costs
Hazard ratios, odds ratios or relative risks for different strategies.
… and so on.

3. Parameterize the Model

We defined many of the underlying parameters earlier in this lecture, so we’ll repeat them briefly here.

3. Parameterize the Model

We start with a healthy population of 25 year olds and follow them until age 100 (or death, if earlier).

Remaining healthy carries no utility decrement (utility weight= 1.0)
Becoming sick carries a 0.25 utility decrement for the remainder of the person’s life (utility weight = 0.75)
Death carries a utility weight value of 0.0.

3. Parameterize the Model

There is no cost associated with remaining healthy.

Becoming sick incurs $1,000 / year in costs.
Becoming sick increases the risk of death by 300%.

3. Parameterize the Model

Each strategy has a different cost and impact on the likelihood of becoming sick.

Strategy	Description	Cost
A	Standard of Care	$25/year
B	Additional 4% reduction in risk of becoming sick	$1,000/year
C	12% reduction in risk	$3,100/year
D	8% reduction in risk	$1,550/year
E	8% reduction in risk	$5,000/year

3. Parameterize the Model

It is critical to follow a formal process for parameterizing your model.

Often, parameters are drawn from the published literature, and it is important to track the source (published value, assumption, etc.) for each model parameter.
- For example, the percent risk reduction parameter for each strategy may come from different clinical trials.
- The parameter governing death from background causes may be derived from mortality data.

3. Parameterize the Model

It is critical to follow a formal process for parameterizing your model.

Some parameters may just be values (e.g., cost of Strategy A is $25/yr)
Some parameters may be functions of other parameters.
- For example, suppose we want to follow a cohort of 25 year olds until age 100 or death, if it occurs earlier.
- In that case we have two “fixed” parameters: the starting age, and the maximum age.
- We can use these two parameters to infer the total number of cycles we need to run.

3. Parameterize the Model

It is critical to follow a formal process for parameterizing your model.

Parameters also have various “flavors”:
1. Probabilities
2. Rates
3. Hazard ratios
4. Costs
5. Utilities
6. etc.

3. Parameterize the Model

It is critical to follow a formal process for parameterizing your model.

All of the above highlight the importance of adopting a formal process for naming and tracking the value, source, and uncertainty distribution of all model parameters in one place.
We recommend a structured approach based on parameter naming conventions and parameter tables.

3. Parameterize the Model

Naming conventions:

type	prefix
Probability	p_
Rate	r_
Matrix	m_
Cost	c_
Utility	u_
Hazard Ratio	hr_

4. Calculate or Define the Transition Probability Matrix

Transition Probability Matrix

	Healthy	Sick	Dead
Healthy	0.856	0.138	0.007
Sick	0	0.982	0.02
Dead	0	0	1

Transition Probability Matrix

It is rarely the case that you will have access to all necessary transition probabilities.

Often, you will curate or define various quantities (e.g., rates, hazard rates, etc.) to construct the transition probability matrix for each strategy under consideration.

4. Run the Model

4. Next up: Decision Trees in Amua